Single-Photon Avalanche Diode Detector Array

ABSTRACT

Example embodiments relate to single-photon avalanche diode detector (SPAD) arrays. One embodiment includes a SPAD array that includes a silicon substrate, a plurality of primary electrodes, and a plurality of secondary electrodes. Each of the primary electrodes includes a semiconductor material of a first doping type, extends in the silicon substrate in a first direction, and has a rotationally symmetric cross-section in a first plane perpendicular to the first direction. The plurality of secondary electrodes includes a semiconductor material of a second doping type and extends parallel to the primary electrodes in the silicon substrate. Further, the silicon substrate includes a doped upper field redistribution layer, a doped lower field redistribution layer, and a doped depletion layer arranged between the upper field redistribution layer and the lower field redistribution layer. A cross-section of each primary electrode is surrounding by one or more cross-sections of at least one neighboring secondary electrode.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a non-provisional patent application claimingpriority to European Patent Application No. EP 19183610.5, filed Jul. 1,2019, the contents of which are hereby incorporated by reference.

FIELD OF THE DISCLOSURE

The present disclosure generally relates to the field of lightdetection. More in particular, the present disclosure relates to lightdetection using an array of single-photon avalanche diodes.

BACKGROUND

A commonly-used technique for single-photon detection is based onsolid-state avalanche photodiodes. Such devices may be operated in theso-called Geiger mode, meaning that individual photo-generated chargesare multiplied into detectable charge packets through impact ionizationin an electric field. When operating in this mode, the detector may bereferred to as a single-photon avalanche diode (SPAD). For manyapplications, including for example range-finding, detectingnear-infrared (NIR) radiation with high efficiency using such SPADdetectors may be important.

To exploit well-established semiconductor processing platforms, and tosimplify on-chip integration of CMOS circuitry, there may be a stronginterest in developing and fabricating arrays of such SPADs in silicon.However, due to the low energy (˜1 eV) of NIR radiation, siliconprovides a small absorption coefficient for such radiation. Therefore, adepleted volume may be used in addition to an electric field. This mayintroduce trade-offs between detection speed, noise, uniformity, andsensitivity. Implementing arrays of SPADs in silicon may thus bechallenging.

SUMMARY

The present disclosure provides a way of overcoming the above challenge.To at least partly achieve this goal, the present disclosure provides asingle-photon avalanche diode (SPAD) array as defined in the independentclaim. Further embodiments of the SPAD array are provided in thedependent claims.

According to one aspect of the present disclosure, the SPAD arrayincludes a silicon substrate. The SPAD array includes a plurality ofprimary electrodes. Each primary electrode includes a semiconductormaterial of a first doping type. Each primary electrode extends in thesilicon substrate in a first direction. Each primary electrode has arotationally symmetric cross-section in a first plane perpendicular tothe first direction. The SPAD array also includes a plurality ofsecondary electrodes. Each secondary electrode includes a semiconductormaterial of a second doping type. Each secondary electrode extendsparallel to the primary electrodes in the silicon substrate. The siliconsubstrate further includes a doped upper field redistribution layer, adoped lower field redistribution layer, and a doped depletion layerarranged between the upper field redistribution layer and the lowerfield redistribution layer. The primary electrodes extend from the upperfield redistribution layer, through the depletion layer and into thelower field redistribution layer of the silicon substrate. Thecross-section of each primary electrode may be approximately uniform inthe depletion layer. The secondary electrodes extend from the upperfield redistribution layer and at least into the depletion layer. Theprimary electrodes and the secondary electrodes are further configuredsuch that the cross-section of each primary electrode is surrounded, inthe first plane, by one or more cross-sections of at least oneneighboring secondary electrode. The primary electrodes, the secondaryelectrodes, and doping concentrations of the various device layers (e.g.the upper field redistribution layer, the lower field redistributionlayer, and the depletion layer) are further configured such that, if asufficiently high reverse potential is applied between each primaryelectrode and the at least one neighboring secondary electrode: a) aresulting electric field near each primary electrode is radially uniformand peaked such that impact ionization (and e.g. charge multiplication)can occur close thereto, and such that a cross-section of the resultingelectric field is uniform throughout a majority of the depletion layer;b) a remaining bulk silicon volume between each primary electrode andthe at least one neighboring secondary electrode is depleted (e.g. fullydepleted, or at least highly depleted, such as in e.g. equal 80% or moreof the volume between the neighboring primary and secondary electrodes);c) the resulting electric field at the upper field redistribution layerand the lower field redistribution layer is not peaked, such that impactionization can be locally suppressed; and d) the primary electrodes areelectrically isolated due to one or more potential barriers formed by(e.g. below and/or between) the plurality of secondary electrodes (e.g.by the secondary electrodes extending deep enough to create such one ormore potential barriers for the primary electrodes during operatingconditions).

The extension of the substrate and various electrodes into the thirddimension may allow to obtain a large photon absorption probabilitywhile maintaining fast transport of photo-generated carriers to anearest device electrode. The electric field present near the primaryelectrode(s) also provides a region in which the photo-generatedcarriers may multiply into detectable charge packets. This may beachieved without using an intrinsic substrate or additional dopedregions in proximity of the electrodes, both of which may causedetrimental effects to the performance and uniformity of the SPAD array.Consequently, the SPAD array of the present disclosure makes possible toresolve the absorption of a single NIR photon in silicon, due to aninternal gain process (avalanche multiplication). This should becontrasted with e.g. detectors used for detection of high-energyradiation such as X-rays or gamma rays (wherein the relevant energy isin the order of MeV). Such devices may instead rely on the high-energyradiation and its ionizing nature in silicon to create electron-holepairs, and the ability to thereby generate multiple charges from asingle high-energy particle. Consequently, such high-energy detectorstypically do not implement any internal gain process in order to amplifya generated carrier. In fact, in high-energy detectors, active measuresmay be used to prevent such a gain process, for example by creating amore uniform electric field between the electrodes without any peaksclose to a primary electrode (i.e. without the field peaks provided bythe geometry, doping, and dimensioning of the SPAD array of the presentdisclosure). Further, to obtain a large breakdown voltage (e.g. above50V), a high-energy detector may resort to the use of sensor arrays witha large pitch (e.g. above 25 μm) and intrinsic doping of the siliconbulk material.

In some embodiments, a diameter of each primary electrode may be between400 nm and 1 μm. The diameter of each primary electrode may for examplebe approximately 700 nm. Such a diameter may e.g. promote theconcentration of the electric field around the primary electrode in thedepletion layer, thereby reinforcing the field peak close to the primaryelectrode due to geometry rather than doping.

In some embodiments, a doping concentration of the depletion layer mayhave a magnitude of between 1e15 cm⁻³ and 1e17 cm⁻³.

In some embodiments, a distance between each primary electrode and theat least one neighboring secondary electrode may be below 3 μm. Such adistance may enable a higher degree of depletion of the depletion layer.

In some embodiments, the length of each primary electrode may beapproximately the same as a length of the at least one neighboringsecondary electrode.

In some embodiments, the secondary electrodes may be arranged such thattheir cross-sections, in the first plane, form a honeycomb pattern, andwherein, in the first plane, the cross-section of each primary electrodeis arranged within a hexagon formed by six neighboring secondaryelectrodes.

In some embodiments, the at least one neighboring secondary electrodemay have a cross-section, in the first plane, shaped like an annulussurrounding the cross-section of each primary electrode. Phraseddifferently, (the cross-section of) each primary electrode may besurrounded by an annulus-shaped (cross-section of a) secondaryelectrode.

In some embodiments, the first doping type may be an n-type doping, andthe second doping type may be a p-type doping.

In some embodiments, a doping concentration of the primary electrodesand a doping concentration of the secondary electrodes may havemagnitudes of between 1e18 cm⁻³ and 1e20 cm⁻³.

In some embodiments, the length of each primary electrode may be between10 μm and 30 μm.

In some embodiments, the secondary electrodes may have cross-sections,in the first plane, equal to the cross-sections of the primaryelectrodes.

In some embodiments, a doping concentration in the depletion layer maybe gradually reduced from that (i.e. the doping concentration) of thesemiconductor material of each primary electrode to that (i.e. thedoping concentration) of the remaining bulk silicon volume. The gradualreduction may occur over a length of between 50 nm and 200 nm.

In some embodiments, a part of the semiconductor material of eachprimary electrode closer to the lower field redistribution layer mayinclude a localized implant of the first doping type.

In some embodiments, one or more of the secondary electrodes mayneighbor more than one of the primary electrodes. Phrased differently,two or more of the primary electrodes may both have a same secondaryelectrode as a neighbor.

In some embodiments, the SPAD array may further include a plurality ofresistive (poly-silicon) tracks. The tracks may electrically connect theprimary electrodes to a common point.

In some embodiments, the SPAD arrays may further include an activereadout circuit for each primary electrode. Each primary electrode maybe electrically connected to the input of a readout circuit.

In some embodiments, multiple closest-neighboring primary electrodes(e.g. 2 or more) may be electrically connected to a single passive oractive readout circuit. The connected SPADs may e.g. effectively behaveas a single SPAD with a larger pitch.

The present disclosure relates to all possible combinations of featuresrecited in the claims. Further features of the various embodiments ofthe present disclosure will be described below using exampleembodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will be described below with reference to the accompanyingdrawings.

FIG. 1A schematically illustrates a unit cell of an embodiment of a SPADarray, according to example embodiments.

FIG. 1B schematically illustrates a unit cell of an environment of aSPAD array, according to example embodiments.

FIG. 1C schematically illustrates a unit cell of a SPAD array, accordingto example embodiments.

FIG. 1D schematically illustrates a unit cell of a SPAD array, accordingto example embodiments.

FIG. 1E schematically illustrates a unit cell of a SPAD array, accordingto example embodiments.

FIG. 1F schematically illustrates a connection network of a SPAD array,according to example embodiments.

In the drawings, like reference numerals will be used for like elementsunless stated otherwise. Unless explicitly stated to the contrary, thedrawings show only such elements that are necessary to illustrate theexample embodiments, while other elements, in the interest of clarity,may be omitted or merely suggested. As illustrated in the figures, thesizes of elements and regions may not necessarily be drawn to scale andmay e.g. be exaggerated for illustrative purposes and, thus, areprovided to illustrate the general structures of the embodiments.

DETAILED DESCRIPTION

Example embodiments will now be described more fully hereinafter withreference to the accompanying drawings. The drawings show exampleembodiments, but the invention may, however, be embodied in manydifferent forms and should not be construed as limited to theembodiments set forth herein; rather, these embodiments are provided forthoroughness and completeness, and fully convey the scope of the presentdisclosure to the skilled person.

With reference to FIGS. 1A to 1F, various embodiments of a SPAD arrayaccording to the present disclosure will now be described in moredetail.

FIGS. 1A and 1B illustrate schematically a unit cell of a SPAD array100. The array 100 includes a silicon substrate 110, in which is formeda plurality of primary electrodes 120 and a plurality of secondaryelectrodes 130. The primary electrodes 120 extend in the substrate 110in the direction indicated by the arrow d. The secondary electrodes 130also extend in the direction indicated by the arrow d, and parallel tothe primary electrodes 120.

The primary electrodes 120 include a semiconductor material of a firstdoping type (e.g. an n-type or p-type doping), and the secondaryelectrodes 130 include a semiconductor material of a second doping type(e.g. a p-type doping or an n-type doping).

As will be described later herein, the primary electrodes 120 haverotationally symmetric cross-sections 122 seen in a (first) plane 140perpendicular to the direction indicated by the arrow d. In theembodiment of the array 100 illustrated in FIG. 1A, the cross-sections122 of the primary electrodes are circular. In the array 100, thesecondary electrodes 130 also have circular cross-sections 132 in theplane 140. The secondary electrodes 130 are arranged such that, in theplane 140, the cross-section 122 of a primary electrode 120 issurrounded by the cross-sections 132 of six secondary electrodes 130.The secondary electrodes 120 are arranged such that their cross-sectionsform a honeycomb pattern in the plane 140, and each primary electrode120 is arranged with its cross-section 122 (symmetrically located)within a hexagon formed by the cross-sections 132 of the surrounding sixsecondary electrodes 130.

Herein, it is of course envisaged that the array 100 does not extendinfinitely in any direction, and that the above configuration of theprimary electrodes 120 within a hexagon formed by surrounding secondaryelectrodes 130 is only valid within the bulk of the array 100 and note.g. close to an outer edge of the array 100. Phrased differently, whenreferring herein to the various electrodes being e.g. periodicallyarranged, it is understood that this applies only to the bulk of thearray 100.

The silicon substrate 110 of the array 100 further includes a dopedupper field redistribution layer 150, a doped lower field redistributionlayer 152, and a doped depletion layer 154 arranged between the upperfield redistribution layer 150 and the lower field redistribution layer152. As can be seen from FIG. 1A, the primary electrodes 120 extend fromthe upper field redistribution layer 150, through the depletion layer154 and into the lower field redistribution layer 152. As can also beseen from FIG. 1A, the secondary electrodes 130 only extend from theupper field redistribution layer 150 and partly into the depletion layer154. The cross-sections 122 of the primary electrodes are approximatelyuniform in the depletion layer 154.

The primary electrodes 120 may for example be negatively doped, i.e. thefirst doping type may be an n-type doping. The primary electrodes 120may then work as cathodes. Likewise, the secondary electrodes 130 mayfor example be positively doped, i.e. the second doping type may be ap-type doping. The secondary electrodes 130 may then work as anodes. Dueto the different charge transport and multiplication properties ofelectrons and holes, such a selection of the first and second dopingtypes may be beneficial.

The diameter of the rotationally symmetric (e.g. circular) cross-section122 of the primary electrodes 120 may be small compared to other designdimensions, for example, below 1 μm. This may ensure that, once areverse potential is applied between the primary electrode 120 and theneighboring secondary electrode(s), the resulting electric field tendsto crowd around the primary electrode 120 (as derived from Coulomb'slaw). Phrased differently, the resulting electric field may be peaked ator close to the primary electrode 120 due to a geometric effect ratherthan doping. Doping may still be used as a tool to enhance or degradethe electric field peak in the various layers 150, 152 and 154. Therotationally symmetric cross-section 122 may further make the resultingelectric field radially uniform over at least a majority of the lengthl₁ of the primary electrode 120.

Herein, the application of a reverse potential (or sufficiently highreverse potential) refers to the presence of a larger voltage on then-type doped electrodes (i.e. cathodes) compared to the voltage on thep-type doped electrodes (i.e. anodes). Moreover, the voltage is equal orlarger to the breakdown voltage of an individual SPAD in the array. Forexample, the SPAD array device may be operated e.g. between 1 V to 5 Vabove the breakdown voltage. The breakdown voltage may, for example,range between 15 V and 40 V depending on implementation. In someembodiments, a breakdown voltage may, for example, be 30 V.

The various electrodes 120 and 130 may be formed directly in the siliconsubstrate 110. It is also envisaged that all or some of the electrodes120 and/or 130 may be formed as e.g. metal rods inserted into or formedin the substrate 110. In case of the latter, a semiconductor material(layer) may surround each such rod. When referring to such an electrodeas having a particular doping type, it is then the surroundingsemiconductor material which is referred to as being doped with asingular doping type.

A doping level within the depletion layer 154 may be high enough tofurther enhance the field around the primary electrode 120 (e.g. aroundthe cathode), and especially in the region 160 wherein the electricfield is peaked such that impact ionization can occur when a reversepotential is applied. The region 160 may be referred to as amultiplication region. It is further envisaged that the multiplicationregion 160 may extend over the entire length l₁ of the primary electrode120, except for at the top and bottom regions of the primary electrode120 located within the upper field redistribution layer 150 and thelower field redistribution layer 152, respectively. It is envisaged thatthe doping concentration within the depletion layer 154 may have amagnitude of between 1e15 cm⁻³ and 1e17 cm⁻³, and that such a dopinglevel may prohibit the depletion region (i.e. the region 162) fromextending very far from the primary electrode 120. Consequently, it isalso envisaged that the pitch p is sufficiently small to still allow forfull, or at least approximately full or high depletion between theprimary electrode 120 and the nearest neighboring secondary electrodes130.

As an example, the separation (pitch) p between a primary electrode 120and its neighboring secondary electrodes 130 (within the plane 140) mayfor example be equal to or less than approximately 3 μm, such as forexample approximately 2 μm. A diameter (of the cross-sections in theplane 140) of the primary electrodes 120 and the secondary electrodes130 may for example be between 400 nm and 1 μm, such as for exampleapproximately 700 nm. If arranging the electrodes 120 and 130 asillustrated in FIGS. 1A and 1B, a first width w₁ of the unit cell mayfor example be approximately 6 μm. A second width w₂ of the unit cellmay for example be approximately 3.5 μm (or 2 μm times the square-rootof three).

Herein, it is envisaged that values such as X+/−10%, or X+/−5%, are tobe considered as being “approximately X.” It is of course also envisagedthat other dimensions, not falling within the above given values, may beused, if the functionality (as will be described later herein) of thearray 100 is maintained.

It is further envisaged that the doping in the depletion layer 154 formsa substantial contrast with the doping in the upper and lower fieldredistribution layers 150 and 152, respectively. The doping in theselayers 150 and 152 may for example be of a doping type and concentrationdifferent from those of the depletion layer 154. The electric field peakis thereby locally reduced around the primary electrode 120 within theselayers 150 and 152. However, the doping is also such that the primaryelectrodes (cathodes) 120 are electrically isolated from each otherthrough potential barriers 164 formed between (and e.g. below) thesecondary electrodes 130 when a reverse potential is applied, asillustrated in FIG. 1B.

It is envisaged that in some embodiments, such as in the SPAD arrayillustrated in and described with reference to FIG. 1A, at least thelower field redistribution layer 152 may have a thickness approximatelyequal to or larger than a distance between a primary electrode 120 andits nearest neighboring secondary electrode(s) 130 (i.e. a thicknessapproximately equal to the pitch p).

Further, as illustrated in FIG. 1A, a further doped layer 158 may beprovided in the substrate 110 below the lower field redistribution layer152. This further layer 158 may for example be of the second dopingtype, and be highly doped (with a doping concentration magnitude equalto or larger than 5e18 cm⁻³). A thickness of this further, highly dopedlayer 158 may be for example anywhere between 0 μm to 750 μm. The highlydoped layer may be not depleted, and an external potential may beapplied to it. In some embodiments, for example, the thickness may be 0μm (i.e. the further layer 158 is non-existing). It may also, in such asituation, be envisaged that such a further layer 158 is created duringmanufacturing of the SPAD array, but removed (e.g. fully etched away) ata later stage before finalizing the array. It is further envisaged that,if such a further layer 158 is present, a length l₁ of the primaryelectrodes 120 are such that the primary electrodes 120 have arelatively large distance from the further layer 158, unless the furtherlayer 158 is to be removed afterwards. Phrased differently, it isenvisaged that the primary electrodes 120 never extends into the furtherlayer 158 when it exists. If the further layer 158 is non-existing,primary and/or secondary electrodes 120 and 130 may extend to the bottomsurface 142 of the lower field redistribution layer 152. If the furtherlayer 158 is non-existing and no electrodes extend to the bottom surface142 of the lower field redistribution layer 152, an external potentialmay be applied to this surface 142.

The length l₁ of the primary electrodes 120 and a length l₂ of thesecondary electrodes 130 may for example be between 10 μm and 30 μm. Asan example, the length l₁ may be approximately 12 μm, and the length l₂may be approximately 10 μm. In some embodiments, such as the SPAD array100 illustrated in FIGS. 1A and 1B, making the primary electrodes 120deeper than the secondary electrodes 130 (i.e. such that l₁>l₂) mayprevent larger field peaks to exist near the bottom of the primaryelectrodes 120. The primary electrodes 120 may for example extend into aregion with a different doping concentration and/or type compared to thesecondary electrodes 130. If the primary electrodes 120 and secondaryelectrodes 130 have a different length, the thickness and dopingconcentration of the lower field redistribution layer 152 may be adaptedsuch that the field is properly redistributed. Likewise, the length l₂of the secondary electrodes 130 should not be too short, i.e. such thatit becomes difficult to electrically isolate the primary electrodes 120by the potential barriers provided below and between the secondaryelectrodes 130.

A doping concentration of the primary electrodes 120 and the secondaryelectrodes 130 may for example have magnitudes of between 1e18 cm⁻³ and1e20 cm⁻³. The doping concentration may be gradually reduced from thatof the semiconducting material of each electrode to that of theremaining bulk silicon volume. The reduction may occur over alength-scale between 50 nm and 200 nm.

FIG. 1C illustrates schematically another embodiment of a SPAD array101. The unit cell of the array 101 is similar to the array 100described above with reference to FIGS. 1A and 1B, except that theprimary electrodes 120 and the secondary electrodes 130 have equal or atleast approximately equal lengths (i.e. l₁≈l₂), and extend to the bottomsurface 142 of the lower field redistribution layer 152. Additionally,the unit cell of the array 101 includes an oxide layer 156 arranged ontop of the upper field redistribution layer 150. Such an oxide layer 156may of course also be provided in an embodiment such as that illustratedin FIGS. 1A and 1B.

FIGS. 1D and 1E illustrate unit cells of additional embodiments of SPADarrays according to the present disclosure. As illustrated in FIG. 1D,it is envisaged that the cross-sections of the various electrodes in thefirst plane 140 may be such that a primary electrode 120 is arrangedwithin a cylindrically shaped, neighboring secondary electrode 130. Thecross-section 122 of the primary electrode 120 is circular within theplane 140, and the cross-section 132 of the secondary electrode 130forms an annulus which encloses the cross-section 122 of the primaryelectrode 120. The cross-section 122 of the primary electrode 120 ishere also circularly shaped, and arranged symmetrically at the center ofthe annulus formed by the cross-section 132. In accordance with thegeometry and doping constraints described in the present disclosure, thediameter of the cross-section 122 of the primary electrode may be small(e.g. below 1 μm), the inner radius of the annulus 132 may be small(e.g. below 3 μm) and the doping concentration between the electrodesmay be selected such that the depletion layer is depleted and theelectric field is highly peaked around the primary electrode (within themultiplication region 160) in the depletion layer when a reversepotential is applied. It may for example be envisaged that the unit cellshown in FIG. 1D is square, such that the first width w₁ equals thesecond width w₂. Other configurations are also possible, e.g. such thatthe unit cell is rectangular with w₁≠w₂.

As illustrated in FIG. 1E, it is envisaged that the cross-sections ofthe various electrodes in the first plane 140 may alternatively bearranged in e.g. rectangular patterns. For example, as illustrated inFIG. 1E, each primary electrode 120 may be surrounded by four (nearest)neighboring secondary electrodes 130, such that their cross-sections 122and 132 together form e.g. a triangular lattice, square, or rectangularlattice. For example, the primary electrodes 120 may be arranged suchthat, in the first plane 140, their cross-sections 122 form arectangular lattice. The secondary electrodes 130 may be arranged suchthat, in the first plane 140, their cross-sections 132 also form arectangular lattice, but shifted from that of the primary electrodes120. The sizes and dimensions of the electrodes may be approximatelyidentical to those of the embodiment illustrated in and described withreference to FIG. 1A., i.e. the primary electrode may be small (e.g.below 1 μm), a distance between a primary electrode and a nearestneighboring secondary electrodes may be small (e.g. below 3 μm), and thedoping concentration between the electrodes may be selected such thatthe depletion layer is depleted and the electric field is highly peakedaround the primary electrode (within the multiplication region 160) inthe depletion layer when a reverse potential is applied. It is envisagedthat in the unit cell shown in FIG. 1E, the widths w₁ and w₂ may beequal (e.g. for square lattices), or different (e.g. for rectangularlattices).

FIG. 1F illustrates an embodiment of a SPAR array, wherein on top of anoxide layer, such as the layer 156 described with reference to FIG. 1C,is provided a connection network in form of a plurality of tracks (e.g.184), to connect the various electrodes together. In this and otherembodiments, the oxide layer 156 may for example be several hundreds ofnanometers thick. For example, the oxide layer 156 may be approximately400 nm, although other thicknesses are also possible.

For example, metal strips/lines/tracks/paths 170 may be provided toconnect secondary electrodes (indicated by filled circles) 130 together.Similarly, metal pads 180 may be provided above primary electrodes(indicated by empty circles) 120, and the pads 180 may in turn beelectrically connected together by a plurality of tracks 184. Each pad180 may be electrically connected to the underlying primary electrode120. The tracks 184 may for example be (highly-resistive) poly-silicontracks. The tracks 184, as visible in FIG. 1F, may form a meanderingpattern. The tracks may further be connected to metalstrips/lines/tracks/paths 182, which may in turn may be connectedtogether such that the primary electrodes 120 are all electricallyconnected to a common point/potential. Such connections formed by thevarious elements 170, 180, 182 and 184 may provide an optimized use ofavailable space.

The tracks 184 may for example also function as passive quenchingresistors. Instead of, or in addition to, quenching resistors, activecircuitry (i.e. based on transistors) could be connected to the primaryelectrodes. The active circuitry may be monolithically integrated on thesame die as the sensor array, and/or integrated on a secondaryelectrically connected die. Some primary electrodes may also beconnected together (and share a same active circuitry).

In summary, the details given above for the various embodiments of aSPAD array according to the present disclosure allows for the followingconditions to be fulfilled when a sufficiently high reverse bias isapplied between the primary and secondary electrodes: the resultingelectric field is radially uniform close to the primary electrodes inthe cross-section of the electrodes; the electric field cross-section isuniform over a large (or majority) portion of the primary electrodes;the electric field may be reproducible between different detectors (i.e.between multiple unit cells) in the SPAD array; the electric field issufficiently high at low biasing conditions while still enabling thedepletion of the remaining part of the device, and the electric field indifferent parts of the device is manageable by locally adapting thedoping type and concentration such that parasitic effects may besuppressed. Also, the electric field close to a primary electrode is(highly) peaked over the majority of the length of the primaryelectrode, which may allow for uniform charge multiplication of carriersoriginating from anywhere within the device.

The person skilled in the art realizes that the present disclosure isnot limited to the embodiments described above. On the contrary, manymodifications and variations are possible within the scope of theappended claims.

Although features and elements are described above in particularcombinations, each feature or element may be used alone without theother features and elements or in various combinations with or withoutother features and elements.

Additionally, variations to the disclosed embodiments can be understoodand effected by the skilled person in practicing the claims, from astudy of the drawings, the disclosure, and the appended claims. In theclaims, the word “comprising” does not exclude other elements, and theindefinite article “a” or “an” does not exclude a plurality. The merefact that certain features are recited in mutually different dependentclaims does not indicate that a combination of these features cannot beused to advantage.

What is claimed is:
 1. A single-photon avalanche diode (SPAD) array comprising: a silicon substrate; a plurality of primary electrodes, wherein: each of the primary electrodes comprises a semiconductor material of a first doping type, each of the primary electrodes extends in the silicon substrate in a first direction, and each of the primary electrodes has a rotationally symmetric cross-section in a first plane perpendicular to the first direction; and a plurality of secondary electrodes, wherein: each of the secondary electrodes comprises a semiconductor material of a second doping type, and each of the secondary electrodes extends parallel to the primary electrodes in the silicon substrate, wherein the silicon substrate further comprises: a doped upper field redistribution layer; a doped lower field redistribution layer; and a doped depletion layer arranged between the upper field redistribution layer and the lower field redistribution layer, wherein the primary electrodes extend from the upper field redistribution layer, through the depletion layer, and into the lower field redistribution layer of the silicon substrate, wherein the secondary electrodes extend from the upper doping layer and at least into the depletion layer, and wherein the primary electrodes and the secondary electrodes are configured such that: a cross-section of each primary electrode is surrounded, in the first plane, by one or more cross-sections of at least one neighboring secondary electrode; and based on doping concentrations of the upper field redistribution layer, the lower field redistribution layer, and the depletion layer, when a sufficiently high reverse potential is applied between each primary electrode and the at least one neighboring secondary electrode: a resulting electric field near the primary electrode is radially uniform and peaked such that impact ionization can occur close thereto and such that a cross-section of the resulting electric field is uniform throughout a majority of the depletion layer; a remaining bulk silicon volume between the primary electrode and the at least one neighboring secondary electrode is depleted; the resulting electric field at the upper and lower field redistribution layers is not peaked such that impact ionization can be locally suppressed; and the primary electrodes are electrically isolated due to one or more potential barriers formed by the plurality of secondary electrodes.
 2. The SPAR array of claim 1, wherein a diameter of each of the primary electrodes is between 400 nm and 1 μm.
 3. The SPAD array of claim 1, wherein a doping concentration of the depletion layer has a magnitude of between 1e15 cm⁻³ and 1e17 cm⁻³.
 4. The SPAD array of claim 1, wherein a distance between each of the primary electrodes and each of the at least one neighboring secondary electrodes is less than 3 μm.
 5. The SPAD array of claim 1, wherein a length of each of the primary electrodes is approximately the same as a length of each of the at least one neighboring secondary electrodes.
 6. The SPAD array of claim 1, wherein the secondary electrodes are arranged such that their cross-sections in the first plane form a honeycomb pattern, and wherein, in the first plane, the cross-section of each of the primary electrodes is arranged within a hexagon formed by six neighboring secondary electrodes.
 7. The SPAD array of claim 1, wherein the at least one neighboring secondary electrode has an annular cross-section in the first plane surrounding the cross-section of the primary electrode.
 8. The SPAD array of claim 1, wherein the first doping type is an n-type doping and the second doping type is a p-type doping.
 9. The SPAD array of claim 1, wherein a doping concentration of the primary electrodes and a doping concentration of the secondary electrodes have magnitudes between 1e18 cm⁻³ and 1e20 cm⁻³.
 10. The SPAD array of claim 1, wherein a length of each of the primary electrodes is between 10 μm and 30 μm.
 11. The SPAD array of claim 1, wherein the secondary electrodes have cross-sections, in the first plane, equal to the cross-sections of the primary electrodes.
 12. The SPAD array of claim 1, wherein a doping concentration in the depletion layer is gradually reduced from that of the semiconductor material of each of the primary electrodes to that of the remaining bulk silicon volume over a length of between 50 nm and 200 nm.
 13. The SPAD array of claim 1, wherein a part of the semiconductor material of each of the primary electrodes that is closer to the lower field redistribution layer comprises a localized implant of the first doping type.
 14. The SPAD array of claim 1, wherein one or more of the secondary electrodes neighbors more than one of the primary electrodes.
 15. The SPAR array of claim 1, further comprising a plurality of resistive (poly-silicon) tracks electrically connecting the primary electrodes to a common point. 